As light travels through a uniform material, such as air, it behaves as a series of plane waves traveling in the direction of propagation. When a plane wave meets an obstruction, it undergoes a change due to interaction with that obstruction. Every unobstructed point on the wavefront of the wave can be considered as a source of a secondary spherical wavelet with the same wavelength and phase as the incident wave. The outgoing wavefront is the combination of all of these wavelets.
For example, if a plane wave that is traveling through water strikes a barrier that has a single small aperture (i.e., no wider than the wavelength), the outgoing wave takes a form similar to the wavefront that would be generated if a pebble were dropped into the water at the aperture. The incident plane wave is said to diffract outwardly from the aperture in a circular pattern. If the barrier contains an aperture that is larger than the wavelength, the wavefront that emerges from the aperture takes a form similar to the wavefront that would be generated if a continuous series of pebbles were dropped in a line in the aperture. As a result, the portion of the incoming wave that is incident upon the aperture appears to pass through substantially unaltered, while the remainder is blocked by the barrier. At the edges of the emerging wave, some diffraction is evident.
Two major regions surround the aperture; a near-field region and a far-field region. The near-field region is the region within one wavelength of the aperture and the far-field region is the region beyond the distance of one wavelength. The form of a wavefront that emerges from an aperture depends upon whether the point of observation is in the near-field region or far-field region. In the near-field region, the aperture is nearly perfectly imaged showing only minor fringes at the edges due to diffraction. As the point of observation is moved beyond one wavelength from the aperture, the fringes becomes more significant. In the far-field, the image of the aperture is diffraction limited. In other words, diffraction increases fringing in the image of the aperture to such an extent that the aperture is no longer perfectly imaged.
In a case in which the barrier contains multiple apertures, the waves that emerge from each aperture interact with one another in the far-field region. These emerging waves undergo constructive and destructive interference based on their relative phases. For example, if the peak of a wave from a first aperture meets a valley of a wave from a second aperture, the two waves will cancel each other out (i.e., destructive interference). No sign of a wave will be apparent at that point. If, however, the peak of the first wave coincides with a peak of the second wave, they will combine constructively resulting in one relatively larger wave at that point. This behavior—destructive and constructive interference—forms the basis for a diffraction grating, which is a repetitive array of objects, either apertures or opaque obstructions, which produce periodic changes to the phase and/or amplitude of an optical wave that emerges from the grating.
There are a variety of different types of fixed diffraction gratings. One type is the one-dimensional (linear) Bragg diffraction. This grating resembles a comb, wherein there is a fixed, uniform spacing between the teeth. This uniform spacing, as well as the width and depth of the teeth, determine the output characteristics of the grating. The linear Bragg grating is designed to diffract light having a specific wavelength into modes that emerge along multiple discrete angles. That specific wavelength is defined to be the “operating wavelength” of the grating. The light that emerges from the grating without deviation from the incident angle is defined to be in the zeroth-order mode. In a transmissive grating, light emerges at the opposite side of the grating from which it entered while in a reflective grating, light emerges from the same side of the grating. The angle of each of the higher-order modes, and the amount of light in each mode, depends on the design of the grating and the wavelength of the incident light.
In contrast to fixed diffraction gratings, tunable diffraction gratings have been developed wherein the spacing between elements can be varied in order to change the performance of the grating and enable operation over a range of wavelengths. Tunable diffraction gratings are able to:                change the distribution of light that emerges in the zeroth and higher-order modes;        change the angles at which the higher-order modes emerge; and        change the wavelength of operation for the grating.        
One example of a tunable diffraction grating is the laterally-deformable first-order grating. In this type of grating, the grating pitch of a single-plane of uniformly-spaced grating elements is mechanically changed through “accordion-like” expansion or compression of the entire grating. Expansion and compression have been applied through various means including mechanical actuators such as piezo-electric elements, MEMS lateral actuators, electromagnetic actuators, and thermal actuators. Unfortunately, laterally-deformable gratings have suffered from non-uniform compression due to mechanical irregularities as well as poor reliability due to large induced strains in the grating materials.
A second type of tunable grating is the vertically-deformable first-order grating. One example of this type of grating is disclosed by Solgaard et al. in “Deformable Grating Light Valve,” Optics Letters, v(17) 1992 (hereinafter referred to as “the Solgaard device”). These gratings comprise two “half-gratings,” each of which has a linear array of grating elements. Each half-grating has a 50% fill-factor and the same half-grating pitch (i.e., the repeat distance of the grating elements in the half-grating). The top grating is laterally shifted by one-half of the half-grating pitch, such that the structure appears to be a continuous sheet of material when viewed from above. In its undeflected state, the respective top surfaces of the two half-gratings are separated by a multiple of one-half of the wavelength of incident light. As a consequence, incident light substantially entirely reflects from the structure (i.e., the outgoing light is in the zeroth-order mode). When the vertical distance that separates the two top surfaces is changed by an amount equal to one-quarter of the incident wavelength, the optical energy is substantially completely diffracted into the negative and positive higher-order modes.
In its deflected state, the Solgaard device operates on the far-field of the emerging light in the same manner as a conventional diffraction grating. Specifically, in the far field, reflected wavelets from each grating element combine constructively and destructively as a function of the relative phase of the multiple wavelet components at each point in space.
In its undeflected state, the Solgaard device approximates a mirror surface due to the 360° phase difference (i.e., one complete wavelength) between the two half-gratings. Light having the same wavelength emanating from two points that are separated by an integer multiple of a wavelength reinforce each other (i.e., combine constructively).
Laterally-deformable diffraction gratings based on MEMS are also known, such as the MEMS reconfigurable optical grating described by Rumpf et al., in U.S. Pat. No. 6,628,851. Rumpf describes a conventional diffraction grating wherein each line-element is attached to an individual lateral actuator in order to enable reconfigurability within the plane containing the conventional line-elements.
The range of motion required for known laterally-deformable or vertically-deformable tunable diffraction gratings is a significant fraction of the operating wavelength of the grating. As a consequence, the speed of response (i.e., operating bandwidth) and reliability of these tunable diffraction gratings are limited by mechanical considerations, such as the size and mass of the line-elements and the amount of induced strain that is required to affect a desired change in operating characteristic.